# Differentiable programming and its applications to dynamical systems

arXiv: https://arxiv.org/abs/1912.08168 · HTML: https://mlsanity.com/paper/1912.08168/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2019.

## Built on by (most cited first, 3 of 3)

- [Differentiable Agent-Based Simulation for Gradient-Guided Simulation-Based Optimization](https://mlsanity.com/paper/2103.12476/) (2021)
- [What You See is Not What You Get: Neural Partial Differential Equations and The Illusion of Learning](https://mlsanity.com/paper/2411.15101/) (2024)
- [Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming](https://mlsanity.com/paper/2606.06094/) (2026)

## Abstract (arXiv)

Differentiable programming is the combination of classical neural networks modules with algorithmic ones in an end-to-end differentiable model. These new models, that use automatic differentiation to calculate gradients, have new learning capabilities (reasoning, attention and memory). In this tutorial, aimed at researchers in nonlinear systems with prior knowledge of deep learning, we present this new programming paradigm, describe some of its new features such as attention mechanisms, and highlight the benefits they bring. Then, we analyse the uses and limitations of traditional deep learning models in the modeling and prediction of dynamical systems. Here, a dynamical system is meant to be a set of state variables that evolve in time under general internal and external interactions. Finally, we review the advantages and applications of differentiable programming to dynamical systems.